[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Newform invariants
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
Refresh table
\( p \)
Sign
\(3\)
\(1\)
\(11\)
\(-1\)
\(61\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{11} + 2 T_{2}^{10} - 14 T_{2}^{9} - 27 T_{2}^{8} + 66 T_{2}^{7} + 125 T_{2}^{6} - 115 T_{2}^{5} - 227 T_{2}^{4} + 40 T_{2}^{3} + 129 T_{2}^{2} + 26 T_{2} + 1 \)
T2^11 + 2*T2^10 - 14*T2^9 - 27*T2^8 + 66*T2^7 + 125*T2^6 - 115*T2^5 - 227*T2^4 + 40*T2^3 + 129*T2^2 + 26*T2 + 1
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2013))\).
$p$
$F_p(T)$
$2$
\( T^{11} + 2 T^{10} - 14 T^{9} - 27 T^{8} + \cdots + 1 \)
T^11 + 2*T^10 - 14*T^9 - 27*T^8 + 66*T^7 + 125*T^6 - 115*T^5 - 227*T^4 + 40*T^3 + 129*T^2 + 26*T + 1
$3$
\( (T + 1)^{11} \)
(T + 1)^11
$5$
\( T^{11} + T^{10} - 33 T^{9} - 40 T^{8} + \cdots + 71 \)
T^11 + T^10 - 33*T^9 - 40*T^8 + 360*T^7 + 567*T^6 - 1464*T^5 - 3069*T^4 + 1227*T^3 + 5533*T^2 + 2989*T + 71
$7$
\( T^{11} + 11 T^{10} + 31 T^{9} - 41 T^{8} + \cdots + 31 \)
T^11 + 11*T^10 + 31*T^9 - 41*T^8 - 267*T^7 - 86*T^6 + 682*T^5 + 449*T^4 - 594*T^3 - 388*T^2 + 62*T + 31
$11$
\( (T - 1)^{11} \)
(T - 1)^11
$13$
\( T^{11} + 13 T^{10} + 7 T^{9} - 493 T^{8} + \cdots + 631 \)
T^11 + 13*T^10 + 7*T^9 - 493*T^8 - 1637*T^7 + 3051*T^6 + 19800*T^5 + 19621*T^4 - 18024*T^3 - 33322*T^2 - 11037*T + 631
$17$
\( T^{11} + 13 T^{10} - 31 T^{9} + \cdots + 626503 \)
T^11 + 13*T^10 - 31*T^9 - 850*T^8 - 178*T^7 + 21208*T^6 + 7094*T^5 - 249851*T^4 + 107457*T^3 + 1203751*T^2 - 1823560*T + 626503
$19$
\( T^{11} + 12 T^{10} - 17 T^{9} + \cdots - 10591 \)
T^11 + 12*T^10 - 17*T^9 - 680*T^8 - 2446*T^7 + 2508*T^6 + 34115*T^5 + 82900*T^4 + 82409*T^3 + 18164*T^2 - 22012*T - 10591
$23$
\( T^{11} + 3 T^{10} - 108 T^{9} + \cdots - 28177 \)
T^11 + 3*T^10 - 108*T^9 - 492*T^8 + 2989*T^7 + 19567*T^6 - 2486*T^5 - 189635*T^4 - 322756*T^3 - 15330*T^2 + 144613*T - 28177
$29$
\( T^{11} - 2 T^{10} - 230 T^{9} + \cdots + 8795203 \)
T^11 - 2*T^10 - 230*T^9 + 458*T^8 + 18422*T^7 - 37583*T^6 - 582271*T^5 + 1281381*T^4 + 5470302*T^3 - 14640462*T^2 + 1078842*T + 8795203
$31$
\( T^{11} - T^{10} - 119 T^{9} + 80 T^{8} + \cdots + 1679 \)
T^11 - T^10 - 119*T^9 + 80*T^8 + 4590*T^7 - 1492*T^6 - 61451*T^5 - 11882*T^4 + 150060*T^3 + 141449*T^2 + 38775*T + 1679
$37$
\( T^{11} + 14 T^{10} - 116 T^{9} + \cdots - 7494199 \)
T^11 + 14*T^10 - 116*T^9 - 1935*T^8 + 4077*T^7 + 87871*T^6 - 54769*T^5 - 1524710*T^4 + 346193*T^3 + 7611417*T^2 - 506455*T - 7494199
$41$
\( T^{11} - 3 T^{10} - 251 T^{9} + \cdots + 337149 \)
T^11 - 3*T^10 - 251*T^9 + 282*T^8 + 21232*T^7 + 17489*T^6 - 610896*T^5 - 1718757*T^4 + 514359*T^3 + 4101417*T^2 + 2614545*T + 337149
$43$
\( T^{11} + 21 T^{10} - 62 T^{9} + \cdots + 512533 \)
T^11 + 21*T^10 - 62*T^9 - 3422*T^8 - 6305*T^7 + 190400*T^6 + 522158*T^5 - 4275267*T^4 - 7899399*T^3 + 36891757*T^2 - 26424338*T + 512533
$47$
\( T^{11} + 16 T^{10} + \cdots - 117544331 \)
T^11 + 16*T^10 - 109*T^9 - 2638*T^8 - 54*T^7 + 142779*T^6 + 250008*T^5 - 3246450*T^4 - 6638539*T^3 + 32576690*T^2 + 47877606*T - 117544331
$53$
\( T^{11} - 412 T^{9} + \cdots - 508890247 \)
T^11 - 412*T^9 - 447*T^8 + 61651*T^7 + 134260*T^6 - 3899798*T^5 - 12518596*T^4 + 83978779*T^3 + 347434637*T^2 + 48963069*T - 508890247
$59$
\( T^{11} - 3 T^{10} - 145 T^{9} + \cdots + 228413 \)
T^11 - 3*T^10 - 145*T^9 + 237*T^8 + 5164*T^7 - 9158*T^6 - 57305*T^5 + 96605*T^4 + 219910*T^3 - 304189*T^2 - 269079*T + 228413
$61$
\( (T - 1)^{11} \)
(T - 1)^11
$67$
\( T^{11} + 24 T^{10} + 9 T^{9} + \cdots + 15755917 \)
T^11 + 24*T^10 + 9*T^9 - 4555*T^8 - 46587*T^7 - 68361*T^6 + 1620889*T^5 + 12275688*T^4 + 39537155*T^3 + 64709417*T^2 + 51580730*T + 15755917
$71$
\( T^{11} - 7 T^{10} - 358 T^{9} + \cdots - 786742397 \)
T^11 - 7*T^10 - 358*T^9 + 2032*T^8 + 46398*T^7 - 200277*T^6 - 2633829*T^5 + 7329633*T^4 + 65170698*T^3 - 47026493*T^2 - 654256122*T - 786742397
$73$
\( T^{11} + 42 T^{10} + 419 T^{9} + \cdots - 10219489 \)
T^11 + 42*T^10 + 419*T^9 - 5038*T^8 - 121073*T^7 - 532434*T^6 + 3774185*T^5 + 40192045*T^4 + 100806196*T^3 + 19264*T^2 - 73411125*T - 10219489
$79$
\( T^{11} + 11 T^{10} - 179 T^{9} + \cdots - 7961 \)
T^11 + 11*T^10 - 179*T^9 - 2200*T^8 + 2192*T^7 + 72080*T^6 + 122679*T^5 - 199924*T^4 - 530869*T^3 - 350186*T^2 - 90207*T - 7961
$83$
\( T^{11} + 34 T^{10} + 251 T^{9} + \cdots - 3176377 \)
T^11 + 34*T^10 + 251*T^9 - 3546*T^8 - 66859*T^7 - 353616*T^6 - 263219*T^5 + 3258112*T^4 + 8789877*T^3 + 3507466*T^2 - 6002691*T - 3176377
$89$
\( T^{11} - 29 T^{10} + \cdots - 371355157 \)
T^11 - 29*T^10 + 27*T^9 + 4919*T^8 - 22551*T^7 - 278670*T^6 + 1616886*T^5 + 5488009*T^4 - 40885576*T^3 - 6205668*T^2 + 308290628*T - 371355157
$97$
\( T^{11} + 45 T^{10} + \cdots + 5102744443 \)
T^11 + 45*T^10 + 309*T^9 - 13719*T^8 - 241814*T^7 - 32222*T^6 + 25384887*T^5 + 170383421*T^4 + 38010704*T^3 - 2061425026*T^2 - 1902380148*T + 5102744443
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